Patterns of Bifurcation Suppressing Escape at Internal Resonance

  • G.H.M. van der Heijden
  • J.M.T. Thompson
Conference paper
Part of the Solid Mechanics and its Applications book series (SMIA, volume 122)


For an archetypal two-degree-of-freedom forced oscillator, relevant to a large class of mechanical problems, we examine the patterns of bifurcation that govem the internal 1:2 resonance of the system. A knowledge of these bifurcations allows the counter-intuitive suppression and control of escape by internal modal interactions. The bifurcations examined include symmetry-breaking pitchforks, Neimark bifurcations (secondary Hopf bifurcations) to a toroidal attractor, and chaotic crises which trigger dangerous large-amplitude excursions. We particularly focus on the effect that a symmetry-breaking imperfection has on the suppression of escape.

Key words

Suppression of escape 2 DOF forced oscillator symmetry breaking 1:2 resonance Neimark bifurcation unfolding 


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Copyright information

© Springer 2005

Authors and Affiliations

  • G.H.M. van der Heijden
    • 1
  • J.M.T. Thompson
    • 1
  1. 1.Centrefor Nonlinear DynamicsUniversity College LondonLondonUK

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